Orthogonal Frequency-Division Multiplexing (OFDM) has become a popular modulation system for wireless communications. It is likely that some variants of OFDM will also be used for 5G standards of the Third Generation Partnership Project (3GPP). OFDM includes modulation schemes based on OFDM, but where the data applied to subcarriers are precoded, e.g. Discrete Fourier Transform Spread (DFTS) OFDM.
In OFDM, a wideband communications channel is divided into a number of narrowband subcarriers. Since each subcarrier is narrowband, the effects of frequency selectivity can be reduced, if a cyclic prefix or guard interval is used they may be eliminated, i.e. data transmitted on one subcarrier does not interfere with data transmitted on other subcarriers.
If the transfer function of a subcarrier is inspected, it may be possible to see that its spectrum roll off is actually rather slow (it roughly decays with 1/frequency^2). The reason that two different subcarriers don't interfere is not that no energy of one subcarrier spreads into another subcarrier but due to the orthogonal properties of the subcarrier functions.
Typically the spectrum roll off achieved by the OFDM subcarrier function alone is not sufficient to meet certain requirements, e.g. the allowed out of band emissions. Therefore, the OFDM waveform is typically filtered to suppress out of band emissions. FIG. 1a shows a block diagram of filtered OFDM where two OFDM numerologies are mixed on the same carrier. The guard interval (GI) can alternatively to a guard interval be a cyclic prefix (CP), a known word etc. (all well known techniques in OFDM modulation). In the following the term guard interval is often used for all these techniques. 5G systems should be capable to support on the same carrier at the same time multiple services with different requirements. In some cases this implies that on the same carrier at the same time multiple OFDM signals, with different numerologies, e.g. subcarrier bandwidth, guard interval length, need to coexist. Subcarriers are then no longer orthogonal but start to interfere with each other. The amount of interference is determined by the spectrum roll off which, as stated earlier, is rather slow for OFDM. In this setup, each OFDM waveform is individually filtered to suppress interference towards subcarriers of the other OFDM numerology/ies.
Instead of (or to complement) filtering, windowing can be applied to the OFDM waveform. FIG. 1b shows a block diagram of windowed OFDM with two OFDM numerologies that share the same carrier. Here a cyclic prefix is used.
FIG. 2 shows a schematic diagram of how windowing is done. The OFDM symbol is cyclic extended (both at the beginning and at the end) and a window is applied at the beginning and end of this extended symbol. Depending on the receiver processing, the cyclic suffix (i.e. the cyclic extension at symbol block end) matches the decaying window slope or is slightly longer. A typical windowed OFDM receiver discards the samples belonging to the windowed slopes and either proceeds with standard OFDM receiver processing or also applies receiver (Rx) windowing. Since the receiver discards the windowed samples, it is possible to overlap the rising slope of the next OFDM symbol with the falling slope of the current OFDM symbol and thus save some overhead, as shown in FIG. 2.
In FIG. 2, a cyclic extension is added both at the beginning and end of the symbol. However, windowing works as well if the cyclic extension is only added at the beginning or at the end (the single cyclic extension should in this case cover for the delay spread as well as windowing at both ends of the symbol, and if windowing at the receiver (Rx) is applied, also for Rx windowing).
Both windowing and filtering smoothen transitions from one OFDM symbol to the next, i.e. waveform discontinuities are reduced. The signal becomes smoother. A smooth time domain signal has less high-frequency components, therefore windowing and filtering improve the spectrum roll off.
The maximum achievable Signal-to-Interference-Plus-Noise Ratio (SINR) of a carrier that transmits OFDM waveforms with narrow and wide subcarriers is increased with windowing or individual filtering of each OFDM waveform. A windowed system achieves much higher SINR than the system without windowing since interference between subcarriers is suppressed. Also, the Power Spectral Density (PSD) of the OFDM subsystem can be studied and the PSDs of windowed waveforms decay much faster than waveforms without windowing.
Modern wireless communication systems use multi-antenna techniques to improve performance. The performance metric can either be data rate, coverage, robustness, or combinations thereof. Spatial multiplexing targets improved throughput, beamforming improved coverage, and transmit diversity improved robustness. Common to many multi-antenna schemes is precoding, i.e. that one signal layer is mapped to multiple antennas or antenna elements. The precoding or antenna weights may depend on the channel. Precoding can be done frequency selective, i.e. different precoding weights are applied to different frequencies, or wideband, i.e. the same precoder is applied across the used bandwidth. Wideband precoders are often implemented in time-domain after OFDM modulation. If applied in time-domain, the precoding can be done either in analogue/digital baseband, at some intermediate frequency, or radio frequency.
As described in the previous section, transmitter (Tx) windowing or filtering helps to make the signal discontinuities smoother and by that improve the spectrum roll off.
At OFDM symbol boundaries, the precoding weights can be changed to adopt to changed channel conditions or if the next symbol is transmitted towards a different receiver or set of receivers. If the precoding weights are applied in frequency-domain or in time-domain prior Tx filtering or windowing the discontinuity introduced by precoder weight switching can be seen as part of the regular discontinuity between OFDM symbols and will be handled by a subsequent Tx filtering or windowing operation.
The situation is different if precoding and changing of precoder weights is done after Tx filtering or windowing. FIG. 3 schematically shows where precoder weights are changed. The PSD of a Tx windowed OFDM system without changing precoders may be compared with a system with changing precoders whereby it can be seen that spectrum regrowth occurs. As shown in FIG. 4, the windowed waveform without precoding (or constant precoder) has a steeper spectrum roll-off. With changing precoding, the PSD of a windowed system is similar to a system without windowing.
The precoder changes introduce signal discontinuities. Since the precoder changes and thus the signal discontinuities happen after Tx windowing or filtering they are not smoothed out but remain as a discontinuity in the transmitted signal. These discontinuities lead to spectrum regrowth.
Changing of precoder weights after TX filtering or windowing typically happens for analogue beamformers (in baseband, Intermediate Frequency (IF), or Radio Frequency (RF)).